Near soliton dynamics and singularity formation for $L^2$ critical problems

Y. Martel   ; F. Merle   ; P. Raphael   ; J. Szeftel

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 69 (2014) no. 2, pp. 261-290

Résumé

This survey reviews the state of the art concerning singularity formation for two canonical dispersive problems: the $L^2$ critical non-linear Schrödinger equation and the $L^2$ critical generalized KdV equation. In particular, the currently very topical question of classifying flows with initial data near a soliton is addressed. Bibliography: 72 titles.

Détail

Keywords: non-linear Schrödinger equation, critical equation, generalized Korteweg–de Vries equation, blowup, blowup profile, qualitative behaviour of solutions, non-linear dispersive equation.
Mots-clés : soliton

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